Unit-1 Quantum Mechanics

8/20/2019 Unit-1 Quantum Mechanics

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UNIT-1 QUANTUM

MECHANICS

TRILOK B AKHANI

HEAD, APPLIED SCIENCESPIT


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What is QuantumM!hani!s"

• Quantum mechanics is th $%&' %( s!inti)! *a+s

that &s!i$ th +a!' $ha.i% %( /h%t%ns, *!t%nsan& th %th /ati!*s that ma u/ th uni.s0

• Quantum mechanics is th $an!h%( physics *atin t% th .' sma**0

•At th s!a* %( at%ms an& *!t%ns, man' %( th2uati%ns %( !*assi!a* m!hani!s, +hi!h &s!i$ h%+thins m%. at .'&a' si3s an& s/&s, !as t% $us(u*0

•

In !*assi!a* m!hani!s, %$4!ts 5ist in a s/!i)! /*a!at a s/!i)! tim0 H%+., in 2uantum m!hani!s,%$4!ts insta& 5ist in a ha3 %( /%$a$i*it'6 th' ha.a !tain !han! %( $in at /%int A, an%th !han! %($in at /%int B an& s% %n0

http://www.livescience.com/47814-classical-mechanics.htmlhttp://www.livescience.com/47814-classical-mechanics.html


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Quantum m!hani!s 7QM8 &.*%/& %. man' &!a&s,$innin as a st %( !%nt%.sia* mathmati!a*

5/*anati%ns %( 5/imnts that th math %( !*assi!a*m!hani!s !%u*& n%t 5/*ain0

Th %iins %( QM !ann%t $ atti$ut& t% an' %n s!intist0Rath, mu*ti/* s!intists !%nti$ut& t% a (%un&ati%n %(th .%*uti%na' /in!i/*s that a&ua**' ain&a!!/tan! an& 5/imnta* .i)!ati%n $t+n 19:: an&

19;:0 Th' a<

1) Quantized properties< Ctain /%/tis, su!h as/%siti%n, s/& an& !%*%, !an s%mtims %n*' %!!u in

s/!i)!, st am%unts, mu!h *i a &ia* that =!*i!s= (%mnum$ t% num$0 This !ha**n& a (un&amnta*assum/ti%n %( !*assi!a* m!hani!s, +hi!h sai& that su!h

/%/tis sh%u*& 5ist %n a sm%%th, !%ntinu%us s/!tum0 T%&s!i$ th i&a that s%m /%/tis =!*i!&= *i a &ia*

+ith s/!i)! sttins, s!intists !%in& th +%& =2uanti3&0=

Three revolutionaryprinciples


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2) Particles of light< Liht !ans%mtims $ha. as a /ati!*0

This +as initia**' mt +ith hash!iti!ism, as it an !%nta' t% >::

'as %( 5/imnts sh%+in that*iht $ha.& as a +a.3) Waves of matter< Matt !an

a*s% $ha. as a +a.0 This an!%unt t% th %uh*' ;: 'as %(5/imnts sh%+in that matt

7su!h as *!t%ns8 5ists as


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?ai*u %( C*assi!a* Ph'si!s

• Th /h'si!a* /hn%mn%n +hi!h5/*ains th (ai*u %( !*assi!a*/h'si!s a

• 1. Blac!ody "adiation

• 2. The Photoelectric #$ect

• 3. The %ydrogen &tom


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t .i&n! (%m s/!tum mitt& $' a $*a!-$%&'at is a $*a!-$%&'"

An %$4!t that a$s%$s a** in!i&nt a&iati%n, i.e. n% @!ti%n

A sma** h%* !ut int% a !a.it' is th m%st /%/u*a an&a*isti! 5am/*0

⇒N%n %( th in!i&nt a&iati%n s!a/s

What happens to this radiation'

• Th a&iati%n is a$s%$& in th +a**s %( th !a.it'• This !auss a hatin %( th !a.it' +a**s•

At%ms in th +a**s %( th !a.it' +i** .i$at at (2un!is!haa!tisti! %( th tm/atu %( th +a**s• Ths at%ms thn -a&iat th n' at this n+!haa!tisti! (2un!'

The emitted (thermal( radiation characterizes

the euili!rium temperature of the !lac*


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Black-body spectrum


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The +ord "ayleigh


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ac*!ody spectrum•B*a!-$%&is &% n%t =@!t= an' in!i&nt a&iati%n

Th' ma' -a&iat, $ut th missi%n !haa!ti3s th

$*a!-$%&' %n*' Th missi%n (%m a $*a!-$%&' &/n&s %n*' %n itstm/atu n%t %n th natu %( th matia*We ,at 3-- ) radiate in the infrared/!0ects at -- * -- start to glo

&t high T4 o!0ects may !ecome hite hot

Wien5s displacement +a

λm T 6 constant 6 2.787 9 1- 3 m.4 or λm ∝ T

?%un& m/ii!a**' $' %s/h St(an 71986 *at !a*!u*at& $'B%*t3mannσ 0F: G 1:− W0m−>0K −0A $*a!-$%&' a!hs thma* 2ui*i$ium +hn th in!i&nta&iati%n /%+ is $a*an!& $' th /%+ -a&iat&, i.e. i( '%u5/%s a $*a!-$%&' t% a&iati%n, its tm/atu iss unti* thin!i&nt an& a&iat& /%+s $a*an!0

:tefan*Boltzmann +a

Poer per unit area radiated !y !lac*!ody R 6 T ;


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Ra'*ih an& ans in th *at 19th !ntu'

&.*%/& a mathmati!a* &s!i/ti%n %( $*a!$%&'a&iati%n $' m%&*in it +ith stan&in +a.s st u/insi& a !a.it'0

Bis i.s th su*t an& a $i( &i.ati%n0JD%nt +%' a$%ut th mathmati!s (% n%+0 Hsth su*t<

>

;BL-TU7(8 &( D ( &( 0

!

yleigh*


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ultraviolet catastrophe a si%us @a+s in th as%nin $' Ra'*ih an& ansm%, th su*t &%s n%t a +ith 5/imnt+%s, it /&i!ts an in)nit n' &nsit' as λ → :

+as tm& th u*ta.i%*t !atast%/h at th tim $' Pau* Ehn(st8

Amnt $t+n th%'an& 5/imnt is %n*' t% $(%un& at .' *%n

+a.*nths0 Th /%$*m is that statisti!s /&i!t anin)nit num$ %( m%&s as λ→:


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Whats +%n +ith th th%'"Ra'*ih an& ans assum& th a&iati%n +asa$s%$& an& mitt& $' %s!i**at%s in th $*a!$%&'

+a**s0

Liht is EM a&iati%n0 EM a&iati%n !an a!!*at*!t%ns0 E*!t%ns in th at%ms %( th $*a!$%&'+a** +i** a!t *i *itt* $a**s %n s/ins 7ham%ni!%s!i**at%s8 +hn '%u /u**J %n thm +ith *iht0

E*!t%ns a$s%$ *iht n'0 N%+ th' a 5!it&0J

A(t a .' $i( tim, th' +i** t i& %( thi 5!ssn'0

Th 5!ss n' ma' !%m %ut at an' .a*i&%s!i**at% (2un!', i00, at an' (2un!' %( *iht

!%s/%n&in t% a .a*i& %s!i**at% n'0


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Ra'*ih an& ans assum& that %n*' +a.*nths+hi!h !%u*& )t insi&J th !a.it' !%u*& 5ist th0

Ra'*ih an& ans assum& that th a&iati%n 5itinth !a.it' +as th sam as th a&iati%n insi&0

Ra'*ih an& ans assum& that th %s!i**at%s !%u*&

*at mit thi n' at an' (2un!'0

a!!%&in t% !*assi!a* /h'si!s

A .a*i&

assum/ti%n0

A .a*i&

assum/ti%n0

A .a*i&

assum/ti%n0


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P*an! s/nt man' 'as in.stiatin $*a!$%&'a&iati%n, an& &is!%.& that h !%u*& 5/*ain th$*a!$%&' a&iati%n &isti$uti%n $' assumin th$*a!$%&' t% $ ma& u/ %( an n%m%us num$ %(%s!i**at%s, +ith a!h %s!i**at% .i$atin at a )5&(2un!', $ut +ith a +i& an 7(%m : t% in)nit'8 %(

/%ssi$* (2un!is0

Sam as Ra'*ih an& ans, s%

(a0

%oever4 the oscillators could not tae on any ar!itraryfreuency. =nstead4 they could oscillate only in integralmultiples of a freuency f hich depended on the!lac!ody temperature.>>

A .%*uti%na'i&a0

P*an!s P%/%siti%n

Th i** t it i it ( h(


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Ths %s!i**at%s mit n' in units %( h(,+hi!h P*an! !a**& =2uanta= %( n'0 A2uantum %( n' is E h(, an& h is !a**&

P*an!s !%nstant Th (a!t that th %s!i**at%s in th !a.it' +a**s!an int!han n' +ith stan&in +a.s%n*' in units %( h( is a &amati! &/atu (%m!*assi!a* /h'si!s0

P*an!s th%' 5/*ain& $*a!$%&' a&iati%n,$ut .n P*an! $*i.& that *at %ns%m$%&' +%u*& !%n!i* $*a!$%&' a&iati%n

+ith !*assi!a* /h'si!s0

N.th*ss, P*an! +%n th 191 N%$* /i3 (% his &is!%.'%( 2uanta0


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H is P*an!s (%mu*a (% $*a!$%&' a&iati%n<

;

; h( -T

BLh ( U7(8 &( D &( 0

! 1−

P*an! +as iht t% $ sus/i!i%us %( it, $!aus +hnh (%un& it, th +as n% th%ti!a* $asis (% it0H%+., it &%s &s!i$ $*a!$%&' a&iati%n

a!!uat*'0

What?s the B=@ =A#& here'

/scillators can oscillate only in integralmultiples of some fundamental freuency.

These oscillators emit energy in units of hf4called (uanta( of energy. & uantum of

energy is # 6 hf.


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=n 1823 ompton sent a !eam of C*

rays ith a non freuency at a!loc of graphite. When they hit thegraphite4 he noticed that thefreuency of the re!ounding D*ray as

loer than the incident D*ray and anelectron as emitted.

omptone$ect


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Th C%m/t%n !t 7a*s%

!a**& Compton scattering8 isth su*t %( a hih-n'/h%t%n !%**i&in +ith a tata/hit, +hi!h *ass*%%s*' $%un& *!t%ns (%mth %ut sh** %( th at%m %m%*!u*0 Th s!att&a&iati%n 5/in!s a+a.*nth shi(t that !ann%t

$ 5/*ain& in tms %(!*assi!a* +a. th%'0 Th!t +as )st &m%nstat&in 19>; $' Athu H%**'

C%m/t%n 7(% +hi!h h!i.& a 19> N%$* Pi3 0

ompton

e$ect

A h H C b d h i f


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Arthur H. Compton observed the scattering of

x-rays from electrons in a carbon target and

found scattered x-rays with a longer

wavelength than those incident upon the target.

The shift of the wavelength increased withscattering angle according to the Compton

formula:

Compton explained and modeled the data by assuming a particle (photon nature for light and applying

conservation of energy and conservation of momentum

to the collision between the photon and the electron. The

scattered photon has lower energy and therefore a longer

wavelength according to the !lanc" relationship.

At a tim 7a*' 19>:s8 +hn th /ati!* 7/h%t%n8 natu%( *iht sust& $' th /h%t%*!ti! !t +as sti**$in &$at&, th C%m/t%n 5/imnt a. !*a an&in&/n&nt .i&n! %( /ati!*-*i $ha.i%0 C%m/t%n+as a+a&& th N%$* Pi3 in 19> (% th =&is!%.' %(

http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod2.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod1.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod1.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod2.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html


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Pair productionEannihilationPai /%&u!ti%n is a /%!ss in +hi!hth n' %( a /h%t%n is !%n.t&

int% st mass0 In this /%!ss, th/h%t%n &isa//as as an *!t%n-/%sit%n /ai is !at&0 Li+is, thn' %( an *!t%n-/%sit%n /ai!an $ !%n.t int% *!t%manti!a&iati%n $' th /%!ss %( /ai

annihi*ati%n0

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Unit-1 Quantum Mechanics

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